Geodesic
On the and Transformations
Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1021-1044

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Denote by C 0 the collection of complex-valued functions which are continuous and compactly supported on (0, ∞). The transformations of the title are defined on C 0 by 1.1 and 1.2 respectively, where Y v (x) is the Bessel function of the second kind, and H v (x) is the Struve function; see [1; 7.5.4(55)]. The two transformations are studied briefly in [6; §8.4]; tables of transform pairs are given in [2; Chapters IX and XI], where it is also stated that, for – , each of the transformations is the inverse of the other. 
Rooney, P. G. On the and Transformations. Canadian journal of mathematics, Tome 32 (1980) no. 5, pp. 1021-1044. doi: 10.4153/CJM-1980-079-4
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[6] 6. Titchmarsh, E. C., Fourier integrals (Oxford, 1948). Google Scholar

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